The current I (in amperes) when 100 volts is applied to a circuit is given by $I = 5 e ^ { - 2 t } \sin t$ where $t$ is the time (in seconds) after the voltage is applied. Approximate the current at $t = 0.6$ second after the voltage is applied. Round your answer to two decimal places.
A) $I ( 0.6 ) \approx 0.75$ ampere
B) $I ( 0.6 ) \approx 0.85$ ampere
C) $I ( 0.6 ) \approx 1.05$ ampere
D) $I ( 0.6 ) \approx 0.65$ ampere
E) $I ( 0.6 ) \approx 0.95$ ampere

Question

The current I (in amperes) when 100 volts is applied to a circuit is given by $I = 5 e ^ { - 2 t } \sin t$ where $t$ is the time (in seconds) after the voltage is applied. Approximate the current at $t = 0.6$ second after the voltage is applied. Round your answer to two decimal places. 
A) $I ( 0.6 ) \approx 0.75$ ampere
B) $I ( 0.6 ) \approx 0.85$ ampere
C) $I ( 0.6 ) \approx 1.05$ ampere
D) $I ( 0.6 ) \approx 0.65$ ampere
E) $I ( 0.6 ) \approx 0.95$ ampere

Quizplus · Accepted Answer

To find the current at $t = 0.6$, substitute $t = 0.6$ into the equation: $I = 5 e^{-2(0.6)} \sin(0.6)$. Calculate $e^{-1.2} \approx 0.3012$ and $\sin(0.6) \approx 0.5646$. Then, $I \approx 5 \times 0.3012 \times 0.5646 \approx 0.85$ amperes.

The Current I (In Amperes) When 100 Volts Is Applied I=5e−2tsin⁡tI = 5 e ^ { - 2 t } \sin tI=5e−2tsint

The Current I (In Amperes) When 100 Volts Is Applied $I = 5 e ^ { - 2 t } \sin t$